2018 — Advanced index modulation techniques for future wireless networks

Advanced Index Modulation Techniques for Future Wireless

Networks

by

Ebrahim SOUJERI

MANUSCRIPT-BASED THESIS PRESENTED TO ÉCOLE DE

TECHNOLOGIE SUPÉRIEURE IN PARTIAL FULFILLMENT FOR THE

DEGREE OF DOCTOR OF PHILOSOPHY

Ph.D.

MONTREAL, JULY 6, 2018

ÉCOLE DE TECHNOLOGIE SUPÉRIEURE

UNIVERSITÉ DU QUÉBEC

BOARD OF EXAMINERS THIS THESIS HAS BEEN EVALUATED BY THE FOLLOWING BOARD OF EXAMINERS

M. Georges Kaddoum, Thesis Supervisor

Department of Electrical Engineering, École de technologie supérieure

M. Mohamed Cheriet, President of the Board of Examiners

Department of Electrical Engineering, École de technologie supérieure

M. François Gagnon, Member of the Jury

Department of Electrical Engineering, École de technologie supérieure

M. Yousef R. Shayan, External Independent Examiner

Department of Electrical and Computer Engineering, Concordia University

THIS THESIS WAS PRESENTED AND DEFENDED

IN THE PRESENCE OF A BOARD OF EXAMINERS AND THE PUBLIC ON 13 JUNE 2018

ACKNOWLEDGEMENTS

I am especially indebted to Prof. Dr. Georges Kaddoum, who has been so supportive of my career goals and who worked actively to provide me with the protected academic time to pursue those goals with his brilliant supervision, continuous support and professional guidance, without which the achievement of this work would not have been possible. Prof. Dr. Kaddoum has taught me more than I could ever give him credit for here. He has shown me, by his example, what a good scientist and person should be.

I am grateful to all of those with whom I have had the pleasure to work during this and other related projects. Each of the members of my Dissertation Committee has provided me extensive personal and professional guidance and taught me a great deal about both scientific research and life in general.

Nobody has been more patient in the pursuit of this project than the members of my family. I would like to thank my loving and supportive wife, Kokab, and my three wonderful children, Hamed, Reyhaneh and Isabelle Abrar, who sacrificed a lot and provided unending inspiration.

TECHNIQUES DE MODULATION D’INDEX POUR LES SYSTÈMES DE COMMUNICATION À HAUT DÉBIT DE DONNÉES

Ebrahim SOUJERI RÉSUMÉ

Dans l’étude de recherche proposée dans cette thèse de doctorat, nous considérons la modu-lation d’index comme un nouvel outil pour améliorer l’efficacité énergétique et spectrale pour les réseaux 5G à venir, y compris des réseaux de capteurs sans fil et l’Internet des objets. Dans ce sens, la modulation spatiale a été proposée par Mesleh et coll. (2008) pour améliorer la capacité des systèmes sans fil a partiellement atteindre la capacité des Systèmes MIMO mais à moindre coût, ce qui est, en fait, une technique qui a attiré beaucoup d’attention au cours des dernières années. En tant que tels, les systèmes SM ont été considérés comme des candidats possibles pour des systèmes de MIMO de prochaine génération à spectre efficace et à économie d’énergie, c’est-à-dire à faible consommation. Cependant, la mise en œuvre de la SM est égale-ment difficile en raison de sa forte dépendance aux caractéristiques du canal, à la corrélation entre des canaux, aux CSI corrompus et à la nécessité d’avoir l’espacement approprié entre les antennes. De plus, le SM nécessite plusieurs antennes à l’émetteur, ce qui ajoute un coût supplémentaire à l’implémentation matérielle. En outre, le nombre de bits mappés dans SM est limité par la taille physique du dispositif connecté au réseau sans fil où seul un petit nom-bre d’antennes peut être utilisé. Le temps de commutation gaspillé par RF des commutateurs d’antenne ajoute à la complexité du problème.

Dans cette thèse, nous étudions les inconvénients du SM dans les articles indiqués ci-dessous, à savoir « Performance comparison of spatial modulation detectors under channel impairments » placé à l’annexe à la fin de la thèse puisqu’il s’agit d’un document de conférence, et « Im-pact of antenna switching time on spatial modulation » qui est mis dans le chapitre 1. Dans le premier article, nous avons montré que les dégradations de canaux ont des impacts sérieux sur le BER performances et sur la capacité du système SM et que le SM est trop sensible aux canaux imparfaits et corrélés. Dans le deuxième article, nous avons démontré que le temps de commutation défini comme le temps nécessaire par le système pour éteindre une antenne et activer une autre, qui est une propriété inhérente des commutateurs industriels RF utilisés dans les systèmes SM, est de l’ordre de nanosecondes et naturellement influence le taux de transmis-sion des systèmes SM en raison de l’introduction de lacunes systématiques à la transmistransmis-sion ou des pauses. Compte tenu de la limitation de vitesse des commutateurs RF pratiques lors des transitions, les technologies basées sur de transition d’antenne comme les systèmes SM sont plafonnées en termes de performances de débit de données. En effet, le débit effectif de SM restera l’otage des développements industriels dans le domaine de commutateurs RF. Cela ap-porte des restrictions aux problèmes de mise en œuvre et de fonctionnement lorsque les débits de données élevés deviennent une nécessité. Il est démontré par l’assemblage de nos résul-tats que le temps de commutation Tsw, qui est une condition pour que les transitions entre les antennes se produisent, dicte restrictions sur le débit de données, la capacité et l’efficacité spec-trale des systèmes SM. En outre, nous proposons des schémas de modulation d’indexation non

basés sur matériels comme modulation d’indice de fréquence, modulation chaotique cohérente et modulation chaotique différentielle non cohérente comme des alternatives potentielles à SM, qui seraient également adaptés aux réseaux de capteurs sans fil et aux applications de l’Internet des choses. À cet égard, nous avons proposé trois articles. Le premier article qui représente la modulation d’indice de fréquence est appelé « Frequency index modulation for low complexity low energy communication networks » est placé dans le chapitre 2 de cette thèse. Dans cet ar-ticle, nous explorons un système de communication multi-utilisateur de faible complexité basé sur la modulation d’indice de fréquence qui convient aux applications de l’Internet des choses et nous montrons qu’un tel système constituerait un excellent candidat pour les applications de capteurs sans fil, où il représente une substitution plus simple pour les architectures basées sur le saut de fréquence, dans lesquelles les houblons portent des morceaux supplémentaires. Le troisième article qui concerne la modulation chaotique cohérente est appelé « Design of an initial condition index chaos shift keying modulation » et se trouve au chapitre 3. Dans cet article, une modulation chaotique cohérente basée sur l’indice de condition initiale est proposée. Cette conception vise à augmenter l’efficacité spectrale et énergétique aux niveaux sans précédent. Le schéma proposé exploite les conditions initiales pour générer différentes séquences chaotiques pour transmettre des extra bits par transmission. Par rapport aux schémas de modulation rivaux, les résultats obtenus dans le travail proposé montrent un taux de transfert de données prometteur et une performance compétitive.

Le dernier article utilise un système de décalage-clé chaotique différentiel non cohérent nommé « Permutation index DCSK modulation technique for secure multi-user high-data-rate commu-nication systems » qui se trouve dans l’annexe II. Dans cette conception originale, où chaque trame de données est divisée en deux tranches de temps dans lesquelles le signal chaotique de référence est envoyé dans le premier intervalle de temps et une réplique permutée de la référence signal multiplié par le bit de modulation est envoyé dans le deuxième créneau tem-porel, nous ciblons l’amélioration de sécurité de données, et l’efficacité énergétique et spec-trale. Dans l’ensemble, compte tenu des exigences élevées en matière de bande passante et d’efficacité énergétique des systèmes futuristes, les mécanismes d’indexation douce suggérés par notre étude sont des candidats réussis avec des résultats prometteurs.

Mots-clés: Communications de cinquième génération, réseaux de capteurs sans fil, Internet des objets, modulation d’indice de fréquence, modulation chaotique de l’indice de condition initiale

ADVANCED INDEX MODULATION TECHNIQUES FOR FUTURE WIRELESS NETWORKS

Ebrahim SOUJERI ABSTRACT

In the research study proposed in this Ph.D Thesis, we consider Index Modulation as a novel tool to enhance energy and spectral efficiencies for upcoming 5G networks, including wire-less sensor networks and internet of things. In this vein, spatial modulation was proposed to enhance the capacity of wireless systems to partially achieve the capacity of MIMO systems but at lower cost, making it a technique that has attracted significant attention over the past few years. As such, SM schemes have been regarded as possible candidates for spectrum- and energy-efficient next generation MIMO systems.

However, the implementation of the SM is also challenging because of its heavy dependence on channel characteristics, channel correlation, corrupted CSI and the need to have adequate spacing between antennas. Moreover, the SM requires multiple antennas at the transmitter which adds cost to the hardware implementation. In addition, the number of mapped bits in SM is limited by the physical size of the wireless device where only small number of antennas can be used. The switching time wasted by RF antenna switches adds to the complexity of the issue.

In this Thesis, we study the drawbacks of SM in the articles indicated, namely Performance

Comparison of Spatial Modulation Detectors Under Channel Impairments that is placed in the

Appendix at the end of Thesis as it is a conference paper, and The Impact of Antenna Switching

Time on Spatial Modulation that is put in Chapter 1.

In the first article, we have shown that channel impairments have serious impacts on the BER performance and on the capacity of the SM system and that the SM is too sensitive to both imperfect and correlated channels.

In the second article, we have demonstrated that the switching time defined as the time needed by the system to turn off an antenna and turn on another one, which is an inherent property of RF industrial switches used in SM systems, is in the order of nanoseconds and naturally influences the transmission rate of SM systems because of introducing systematic transmission gaps or pauses. Given the speed limitation of practical RF switches in performing transitions, antenna transition-based technologies like SM schemes are capped in terms of data rate perfor-mance. In fact, the effective data rate of SM will remain hostage to developments in industrial RF switches. This brings restrictions to the implementation and operation issues when ex-tremely high data rates become a necessity. It is shown by the assemblage of our results that the switching time Tsw which is a requirement for transitions between antennas to happen, dic-tates restrictions on data rate, capacity and spectral efficiency of SM systems.

Furthermore, we propose baseband non-hardware-based indexing modulation schemes based on frequency-index modulation, coherent chaotic modulation and non-coherent differential chaotic modulation schemes as potential alternatives to SM, that would also fit wireless sensor networks and internet of things applications. In this regard, we have proposed three articles. The first article which represents frequency index modulation is called Frequency Index

Mod-ulation for Low Complexity Low Energy Communication Networks and is placed in Chapter 2

of this Thesis.

In this article, we explore a low complexity multi-user communication system based on fre-quency index modulation that suits Internet of Things (IoT) applications and we show that such a system would constitute an excellent candidate for wireless sensor applications, where it represents a simpler substitution for frequency-hopping (FH) based architectures, in which the hops carry extra bits.

The third article which concerns coherent chaotic modulation is called Design of an

Initial-Condition Index Chaos Shift Keying Modulation and is located in Chapter 3.

In this article, an initial condition index chaos shift keying modulation is proposed. This design aims to increase the spectral and energy efficiencies to unprecedented levels. The proposed scheme exploits the initial conditions to generate different chaotic sequences to convey extra bits per transmission. In comparison to rival modulation schemes, the results obtained in the proposed work show a promising data rate boost and a competitive performance.

The last article employs a non-coherent differential chaotic shift-key system named

Permuta-tion Index DCSK ModulaPermuta-tion Technique for Secure Multi-User High-Data-Rate Communica-tion Systems that is found in the Appendix.

In this original design, where each data frame is divided into two time slots in which the reference chaotic signal is sent in the first time slot and a permuted replica of the reference signal multiplied by the modulating bit is sent in the second time slot, we target enhancing data security, energy and spectral efficiencies.

Overall, in light of the high demands for bandwidth and energy efficiencies of futuristic sys-tems, the suggested soft indexing mechanisms are successful candidates with promising results.

Keywords: 5G Communications, Wireless Sensor Networks, Internet of Things, Frequency-Index Modulation, Initial Condition-Frequency-Index Chaotic Modulation

TABLE OF CONTENTS

Page

INTRODUCTION . . . 1

CHAPTER 1 THE IMPACT OF ANTENNA SWITCHING TIME ON SPATIAL MODULATION . . . 21 1.1 Introduction . . . 21 1.2 System Model . . . 23 1.3 Analytical View . . . 24 1.3.1 Effective SM Capacity . . . 25 1.3.2 Restrictions onβ ... 26 1.3.3 Spectral Efficiency . . . 27

1.4 Discussions and Numerical Results . . . 28

1.5 Conclusions . . . 31

CHAPTER 2 FREQUENCY INDEX MODULATION FOR LOW COMPLEXITY LOW ENERGY COMMUNICATION NETWORKS . . . 33

2.1 Introduction . . . 34

2.2 System Model . . . 37

2.2.1 The Transmitter . . . 37

2.2.2 Total Mapped Bits pT . . . 38

2.2.3 The Receiver . . . 41

2.3 FIM Performance Analysis . . . 42

2.3.1 BER Analysis of FIM . . . 42

2.3.2 Erroneous Active Subcarrier Index Detection Ped . . . 44

2.3.3 BER of Mapped and Modulated Bits . . . 47

2.4 Energy Efficiency, PAPR and Complexity . . . 48

2.4.1 Energy Efficiency . . . 48

2.4.2 PAPR Analysis . . . 49

2.4.3 System Complexity . . . 50

2.5 Simulation Results . . . 51

2.5.1 Performance of FIM . . . 52

2.5.2 Performance Comparison with SM and OFDM-IM Systems . . . 54

2.5.3 Energy Efficiency, PAPR and Complexity Analysis . . . 56

2.5.3.1 Energy Efficiency and PAPR Analysis . . . 56

2.5.3.2 System Complexity . . . 58

2.6 Conclusions . . . 59

CHAPTER 3 DESIGN OF AN INITIAL-CONDITION INDEX CHAOS SHIFT KEYING MODULATION . . . 61

3.1 Introduction . . . 62

3.3 Probability of Error for Mapped Bits . . . 66

3.4 BER Performance Analysis of the ICI-CSK System . . . 66

3.5 Simulation and Evaluation . . . 67

3.6 Conclusions . . . 69

CONCLUSION AND RECOMMENDATIONS . . . 71

APPENDIX I PERFORMANCE COMPARISON OF SPATIAL MODULATION DETECTORS UNDER CHANNEL IMPAIRMENTS . . . 77

APPENDIX II PERMUTATION INDEX DCSK MODULATION TECHNIQUE FOR SECURE MULTI-USER HIGH-DATA-RATE COMMUNICATION SYSTEMS . . . 93

LIST OF TABLES

Page Table 1.1 Capacity and switching parameters vs. antenna setup . . . 30 Table 2.1 FIM transmits a total of pT mapped bits using

NBnumber of sub-bands with N frequencies each . . . 39

Table 2.2 Comparison, OFDM, OFDM-IM and FIM systems for the

LIST OF FIGURES

Page

Figure 0.1 3-D signal constellation for SM systems with M= 4 and Nt= 4 ... 5

Figure 0.2 The concept of switching time and its influence on the system performance . . . 8

Figure 0.3 CIM-SS system model: (a) Transmitter (b) In phase receiver structure Taken from Kaddoum et al. (2015b) . . . 10

Figure 1.1 Block diagram of the SM transmitter . . . 23

Figure 1.2 The effective SM data rate versus SM symbol rate . . . 29

Figure 1.3 Capacities of MIMO, SM and SIMO systems . . . 30

Figure 1.4 SM Spectral efficiencyη versus β for various values of Nt . . . 31

Figure 2.1 Block diagram of the general structure of FIM communication system: a) the transmitter, and b) the receiver . . . 40

Figure 2.2 A given FIM system with 4 subcarriers. In the illustration, the transmitter has indexed the message 01 and transmits the rest of the message via the subcarrier f2only . . . 41

Figure 2.3 Performance of the proposed system with various values of M and N that facilitate the conveyance of 7 bits per transmission . . . 53

Figure 2.4 Performance of the proposed FIM system with various modulation order M for N= 4 subcarriers per sub-band... 53

Figure 2.5 Performance of the proposed FIM system for various subcarriers per sub-band and a modulation order of M= 8 ... 54

Figure 2.6 Performance of FIM in comparison to SM and OFDM-IM for the transmission of a total of 3 bits (mapped and modulated) . . . 55

Figure 2.7 CCDFs of the PAPR of the proposed FIM system with complementing NBand N combinations for NFIM= 64 ... 57

Figure 2.8 Complexity comparison of the proposed FIM, conventional OFDM and OFDM-IM(n,k) systems using a number of subband NB = 1 and FFT-length NFIM= NNB. . . 59

Figure 3.1 A general scheme of the proposed ICI-CSK architecture: (a)

transmitter and (b) receiver . . . 64 Figure 3.2 BER performance of ICI-CSK compared to SM and M-ary PSK for

LIST OF ABREVIATIONS

AWGN Additive White Gaussian Noise

BER Bit Error Rate

BPSK Binary Phase Shift Keying

BS Base Station

CDF Cumulative Density Function

CDMA Code Division Multiple-Access

CIM Code Index Modulation

CM Channel Model

CMOS Complementary Metal–Oxide–Semiconductor

CP Cyclic Prefix

CS Code Shifted

CSD Chaotic Symbolic Dynamic

CSI Channel State Information

DBR Data Energy to Bit Energy Ratio

DCSK Differential Chaos Shift Keying

DF Decode and Forward

ESIM Enhanced Subcarrier Index Modulation

ETS École de Technologie Supérieure

FFT Fast Fourier Transform

FH Frequency Hopping

FIM Frequency Index Modulation

FM Frequency Modulation

FPGA Field-Programmable Gate Array

IAS Inter-Antenna Synchronization

ICI-CSK Initial Condition-Index Chaotic Shift Keying

ICT Information and Communication Technology

IEEE Institute of Electrical and Electronics Engineers

IM Index Modulation

IoT Internet of Things

ISM Industrial Scientific and Medical

LED Light Emitting Diode

LLR Log-Likelihood Ratio

LPI Low Probability of Interception

MA Multiple-Access

MEMS Micro Electro Mechanical Systems

MFSK Multiple Frequency-Shift Keying

MIMO Multiple-Input Multiple-Output

XIX

ML Maximum Likelihood

MMSE Minimum Mean Square Error

MQAM M−ary Quadrature Amplitude Modulation

Msps Mega symbols per second

MU Multiuser

NR Noise Reduction

OD Optimum Detection

OFDM Orthogonal Frequency Division Multiplexing

OM Orthogonal Multilevel

OQPSK Offset Quadrature Phase Shift Keying

PAPR Peak-to-Average Power Ratio

PDF Probability Density Function

PI Permutation Index

PPP Public Private Partnership

QCSK Quadrature Chaos Shift Keying

QPSK Quadrature Phase Shift Keying

RCG Repeated Chaotic Generators

RF Radio Frequency

SER Symbol Error Rate

SIMO Single-Input Multiple-Output

SISO Single-Input Single-Output

SLED Square-Law Envelope Detector

SM Spatial Modulation

SME Small and Medium Enterprise

SS Spread Spectrum

SSK Space-Shift Keying

STBC Space-Time Block Codes

TR Transmitted Reference

UWB Ultra Wide Band

WBAN Wireless Body Area Networks

WSN Wireless Sensor Networks

ZF Zero Forcing

INTRODUCTION

The fifth generation (5G) Infrastructure Public Private Partnership known as the 5G-PPP is a joint initiative between the European Commission and European information and communica-tions technology (ICT) manufacturers, telecommunicacommunica-tions operators, service providers, small or medium-sized enterprises (SMEs) and researcher Institutions. The 5G-PPP is now in its sec-ond phase where 21 new projects were recently launched in Brussels in 2017. The 5G PPP will deliver solutions, architectures, technologies and standards for the ubiquitous next generation communication infrastructures of the coming decade across the globe. The challenge for the 5G Public Private Partnership (5G PPP) is to secure leadership in the particular areas where there is potential for creating new markets such as smart cities, e-health, intelligent transport, education or entertainment and media. The 5G PPP initiative will reinforce the success of the telecommunications industry in global markets and open new innovation opportunities. Ac-cording to European Commission & European ICT Industry (2014), it will open a platform that helps reaching the common goal to maintain and strengthen the global technological lead. The key challenges for the 5G Infrastructure PPP may be summarized as

- Providing 1000 times higher wireless area capacity and more varied service capabilities compared to 2010;

- Saving up to 90% of energy per service provided. The main focus will be in mobile commu-nication networks where the dominating energy consumption comes from the radio access network;

- Reducing the average service creation time cycle from 90 hours to 90 minutes.

- Creating a secure, reliable and dependable Internet with a zero perceived downtime for services provision;

- Facilitating very dense deployments of wireless communication links to connect over 7 trillion wireless devices serving over 7 billion people;

- Ensuring for everyone and everywhere the access to a wider panel of services and applica-tions at lower cost.

0.1 Modulation for 5G Wireless Communications

Concerning the physical layer and the modulation techniques involved therein, Orthogonal Frequency Division Multiplexing (OFDM) is known to be the main platform for 5G wireless communications modulation. But as OFDM has a set of drawbacks like the need to a cyclic prefix (CP), side-lobe frequencies, peak to average power ratio (PAPR) and high sensitivity to carrier frequency offsets, a new technique called Filter Bank Multi-Carrier (FBMC) has been developed to compensate the deficiencies of OFDM and to offer ways of overcoming the known limitations of OFDM of reduced spectral efficiency and strict synchronization requirements. These advantages have led it to being considered as one of the modulation techniques for 5G communication systems Schellmann et al. (2014); Wunder et al. (2014). Note that FBMC is a development of OFDM, which uses banks of filters that are implemented, typically using digital signal processing techniques. Furthermore, when carriers are modulated in an OFDM system, side-lobes spread out either side. With a filter bank system, the filters are used to remove these side-lobes and much cleaner carriers are obtained. FBMC is, however, more complex than OFDM and less flexible for multiple-input multiple-output (MIMO) applications. In addition, OFDM has been around for more than 3 decades and is already incorporated into many platforms in various applications, therefore, any shift to a newer technology like FBMC will need time.

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0.2 Index Modulation

Since 5G wireless networks have drawn great attention over the past few years Andrews et al. (2014), Wang et al. (2014) as the wireless infrastructure for the future, research is ongoing to further enhance this yet to-be implemented technology in terms of bandwidth, data rate and la-tency. Since almost everything will be connected to the internet in what is known as the Internet of Things (IoT) Weber & Weber (2010), it is necessary to develop novel spectrum and energy efficient physical layer techniques for 5G wireless communication networks. Some techniques such as massive MIMO systems, millimetre wave (mmWave) communications and flexible waveform designs have already been developed; however, research community is still working to propose new and more influential physical layer solutions toward 5G wireless networks. The Index Modulation (IM) technique, which considers innovative ways to convey extra in-formation bits compared to traditional communication systems, appears as a competitive can-didate for next generation wireless networks due to the attractive features it offers in terms of spectral and energy efficiencies as well as hardware simplicity. The interest in IM techniques has grown in the past few years as it augments energy and spectrum efficiencies while remain-ing simple and beremain-ing possible to merge with theoretically any digital modulation technique. IM accommodates substitute manners to transfer extra information compared to classical dig-ital modulation schemes that depend on amplitude, phase or frequency of a sinusoidal carrier signal for communication.

In fact, IM schemes map extra information bits by altering the on/off status of an entity in the communication system into which it is merged, such as transmit antennas, subcarriers, radio frequency (RF) mirrors, transmit light emitting diodes (LEDs), relays, modulation types, time slots, precoder matrices, dispersion matrices, spreading codes, signal powers, etc. Brief, IM establishes totally novel dimensions for data transmission.

In IM, a considerable part of the outgoing bits are inherently transmitted, so their transmission energy is saved and transferred to the actually –physically– transmitted bits, which results in an improved error performance compared to classical schemes that utilise the same total transmission energy. That is to say, IM schemes convey extra information in an energy-efficient fashion.

As IM suggests new dimensions for conveying digital information, the spectral efficiency of the considered communication system can be effectively enhanced without increasing hardware complexity. In the following sections, we will have a glance at spatial modulation, code index modulation, frequency index modulation and initial-condition chaos shift keying modulation as examples of concern of IM.

0.3 Spatial Modulation

SM is a technique in which indices of the transmit antennas of a MIMO architecture are used for conveying additional information, and is indeed one of the earliest applications of IM, where it represents a novel method to transmit information by means of the indices of the transmit antennas of a MIMO architecture in addition to the conventional M−ary signal constellations. In fact, SM appeared in some works like Chau et al. (2001) and Haas et al. (2002) for the first time but under different names and terminologies, however, the term spatial modulation is utilised for the first time in the studies of Ganesan et al. (2006) and Mesleh et al. (2006a). To be specific, two information-carrying units exist in SM, the indices of the available trans-mit antennas and the M−ary constellation symbols. For each transmission interval, a total of log₂(Nt) + log2(M) outgoing bits enter the transmitter of an SM system, where Nt is the num-ber of antennas in the transmit antenna array and M is the modulation order. To provide some detail, the first log₂(M) bits of the outgoing bit sequence are used to modulate the phase and/or amplitude of a carrier signal, while the remaining log₂(Nt) bits of the outgoing bit sequence

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are considered for the selection of the index of the active transmit antenna that will be turned on to perform the transmission of the corresponding modulated signal. A 3-dimensional con-stellation diagram of SM with Nt = 4 antennae and Quadrature Phase Shift Keying (QPSK) constellation M= 4 is shown in Figure 0.1.

Figure 0.1 3-D signal constellation for SM systems with M= 4 and Nt= 4

Note that a simpler implementation of the SM that relies only on antenna indices and does not incorporate any signal modulation that is known as space-shift keying (SSK) is investigated and developed by Jeganathan et al. (2008b), Jeganathan et al. (2009). Compared to SM, SSK requires neither in-phase and quadrature (IQ) modulation nor pulse shaping, and thus, has a simpler form and less complexity.

0.3.1 SM Receiver

The receiver of the SM scheme has to deal with the following two major tasks: detection of the active transmit antenna for the demodulation of IM bits and detection of the data symbol transmitted over the activated transmit antenna for the demodulation of the bits mapped to the M−ary signal constellation. As a matter of fact, the optimum ML detector of SM has to jointly search over all transmit antennas and constellation symbols to decode both of the bits. Although the suboptimal detector can obtain a significant complexity reduction for increasing number of transmit antennas and higher order constellations, its error performance is consid-erably worse than that of the ML detector. Therefore, the implementation of the suboptimal detector can be problematic for critical applications that require a low error rate. Addition-ally, the sparse structure of SM transmission vectors paves the way for the implementation of near/sub-optimal low-complexity detection methods for SM systems such as matched filter-based detection Tang et al. (2013) and compressed sensing (CS)-filter-based detection Yu et al. (2012).

0.3.2 Features and Drawbacks of SM

In light of the above discussion on the concept of SM, MIMO systems employing SM provide attractive advantages over their traditional counterparts Di Renzo et al. (2016). The main advantages of SM over classical MIMO systems could be summarized as Basar et al. (2017):

- High spectral efficiency: The spectral efficiency of SM is superior to that of traditional single-input single-output (SISO) systems as well as orthogonal space-time block codes (STBCs) due to indexing the transmit antenna number as a supplementary approach of ferrying extra information;

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- High energy efficiency: The SM transmitter power consumption is unconnected to the num-ber of transmit antennas, while the information can still be transferred via these antennas. In fact, SM may be regarded as a green and energy-efficient MIMO technology as it may deploy a transmission system without requiring additional transmission energy but by using a higher number of transmit antennas;

- Simple transceiver design: One RF chain is sufficient for the SM scheme compared to MIMO where many are required, as SM activates a single antenna during a given transmis-sion;

- Elimination of Inter-antenna synchronization (IAS) and inter-channel interference.

While the SM scheme has the aforementioned appealing advantages, it also has some disad-vantages, which are summarized as follows:

- It is mainly solely suitable for base stations of wireless networks, where space is abundant to host multiple antennas. This is because smaller devices such as cell phones do not have the necessary physical space to provide, especially considering that a spacing ofλ/2 between antennas must be respected, whereλ is the transmission wavelength;

- SM is also not applicable to sensor networks and IoT devices as most these devices are tiny and may not have the physical space to handle multiple antennas;

- The spectral efficiency of SM increases logarithmically with Nt;

- The channel coefficients of different transmit antennas have to be sufficiently different for an SM scheme to operate effectively. In other words, SM requires rich scattering environ-ments to ensure better error performance. This requirement is not guaranteed and renders SM impractical;

- The decoding complexity of the SM receiver, in terms of the total number of real multipli-cations, grows linearly with the product of the constellation size and the number of transmit antennas;

- Another impediment of SM techniques is switching time existing in current RF switch modules. Turning antennas on and off is costly in terms of power required for ’on-off’ and the time duration needed for such repetitive ’on-off’ operations to take place, as shown in Fig. 0.2. In fact, switching time intervals introduce systematic transmission gaps in SM systems which overshadow its overall communication performance. In this regard, parasitic antennas which rely on Micro Electro Mechanical Systems (MEMS) technology for RF applications that are being used in handheld mobile devices nowadays have switching times in the range of 2− 50μs which renders it inefficient for today’s high-speed applications, if the antenna is to be switched on and off thousands or millions of times every single second. Indeed, since SM may require a transition (switching) to happen for the transmission of each individual symbol to materialize, it is clear that switching times in antenna controllers must be significantly smaller than the symbol period. This requirement makes the application of MEMS-based technology of today in SM very hard.

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Considering the advantages and disadvantages of SM systems mentioned above, we may con-clude that SM scheme provides an interesting trade-off among encoding/decoding complexity, spectral efficiency, and error performance, however, further technological advancement espe-cially in RF switching techniques is needed before its full implementation.

0.4 Code Index Modulation

A new technique that uses the index modulation domain is developed in Kaddoum et al. (2015b) where the spreading code domain is used as an indexing parameter in order to in-crease the data rate without adding extra computations complexity to the system. This scheme, which is called code index modulation-spread spectrum (CIM-SS), may also be integrated with MIMO or SM systems to achieve higher throughput. CIM-SS uses spreading codes to map additional outgoing data in conjunction with constellation symbols. A system model incorpo-rating the CIM-SS transmitter and receiver structures extracted from Kaddoum et al. (2015b) is shown in Fig. 0.3.

The basic form of CIM-SS considers the outgoing data in pairs, where for each pair of bits, one bit chooses a spreading code from a pre-assigned set of codes, and the other bit is spread by the selected code. At the receiver, the spreading code is first detected which allows the recovery of the mapped bit then the transmitted bit is demodulated via despreading. With this elegant scheme, only half of the bits are physically transmitted over the channel and the other half are mapped into spreading codes. Consequently, CIM-SS increases throughput and decreases energy consumption while retaining the system easy to implement. Furthermore, the gains of the spread spectrum modulation are maintained in the proposed CIM-SS scheme.

In fact, CIM-SS is among the earliest soft-indexing techniques that appeared as a rival for the hardware-based SM technique. A generalized form of this technique which uses M−ary constellation instead of a binary one is developed in Kaddoum et al. (2016b).

Figure 0.3 CIM-SS system model: (a) Transmitter (b) In phase receiver structure Taken from Kaddoum et al. (2015b)

0.5 Frequency Index Modulation

Within the context of soft-index modulation, subcarrier index modulation (SIM) scheme has been proposed in Abu-Alhiga & Haas (2009) where it has been merged with orthogonal fre-quency division multiplexing (OFDM) to constitute SIM-OFDM. Moreover, enhanced subcar-rier index modulation (ESIM) has been proposed to avoid the propagation of error by replacing the concept of majority counting by a simpler method in which a pair of off-on or on-off subcar-riers is used to represent a single bit Tsonev et al. (2011), however, the fact that two subcarsubcar-riers are used to transmit a single bit doubles the required bandwidth necessary for transmission in this method.

11

Eventually, a transmission scheme called OFDM with index modulation (OFDM-IM) is pro-posed Ba¸sar et al. (2013). In this scheme, information is conveyed not only by M-ary signal constellations as in classical OFDM, but also by the indices of the subcarriers, which are ac-tivated according to the incoming information bits. But from the practical point of view, the implementation of this scheme is difficult as it relies on the maximum likelihood (ML) de-tection that requires heavy computing charges as it needs to search over all the possibilities (subcarrier combinations) within a bandwidth. This is costly as it makes a joint search over all possibilities Ba¸sar (2015) and is impractical for large combination values due to its exponen-tially growing decoding complexity Ba¸sar et al. (2013), which makes it unsuitable for WSN applications. Furthermore, the Log-Likelihood Ratio (LLR) detection strategy is another de-tection method proposed for this scheme for high number of subcarriers, but this detector may produce an undefined set of active indices not at all included in the original mapping table Ba¸sar et al. (2013).

In the work of Soujeri et al. (2017), a modified frequency index modulation (FIM) scheme that is simpler than the approach of Ba¸sar et al. (2013) is introduced. This system has a lower complexity compared to OFDM-IM, lower power consumption profile and does not sacrifice data rate as it makes use of the frequency hops in a smart and wise way. As the proposed system does not use all of the available subcarriers, it will also enjoy inter-carrier interference -free transmission while it allows the transmission of additional bits in the index domain. Therefore, this work is an excellent choice for WSNs and IoT applications.

In the FIM scheme, the OFDM bandwidth is divided into equal NBsub-bands of N subcarriers each. A message is divided into mapped and modulated blocks where the mapped block acti-vates a single corresponding subcarrier in its predefined sub-band in order to carry the data of the modulated block. At the receiver side, FFT is first performed on the received signal fol-lowed by sub-sectioning the bandwidth into NB sub-bands where square-law envelope detector

(SLED) is used in each sub-band to identify the active subcarrier. Then, the mapper chooses the corresponding indexed message and demodulates the received signal over the channel to get the remainder. The FIM system keeps the architecture simple and constitutes an excel-lent substitution for the conventional frequency-hopping (FH) technique in which hops carry no additional information. Despite the simplicity, FIM enjoys all the specifications associ-ated with frequency hopping systems from the signal, interference, channel and anti-jamming points of view. Furthermore, the system has a low PAPR profile and may be used in multi-user or multi-node scenarios thanks to OFDMA multiple access technique. These properties make FIM scheme suitable for WSNs and IoT applications as size, simplicity and efficiency are of great importance in these schemes Barnaghi et al. (2012).

While the structure of FIM introduces an important enhancement to personal area networks like Bluetooth and ZigBee, it is quite competitive in high speed 5G networks like UWB and Wi-Fi architectures too.

Q. What is the cost of transmission in terms of Hz/bits in FIM systems?

For the transmission of bmap mapped and bmap modulated bits, a total of btot = bmap+ bmod

bits is transmitted in a FIM system such that, for NBsub-bands, the symbol time TFIMbecomes TFIM= NBbtot.

As the frequency separation between subcarriers must be at least 1/TFIMto respect

orthogonal-ity, the total bandwidth requirement per bit will be

NFIM/TFIM= NBN/NB(bmap+ bmod) = N/btot Hz / bits.

This may be verified for any choice of N, bmap and bmod.

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0.6 Chaotic Index Modulation

0.6.1 A Comprehensive Overview of Chaotic Modulations

Due to their highly non-linear dynamics, chaotic maps may produce infinite number of signals using different initial conditions. In fact, the sensitivity of chaotic maps upon initial conditions is very high and the produced chaotic signals show very low cross-correlation values that qual-ify such sequences to be used in spread spectrum applications. In this vein, chaotic spreading sequences can be considered as suitable candidates for spread spectrum applications Kaddoum (2016b).

In fact, chaos-based modulation provides the advantages of conventional spread-spectrum sys-tems like jamming resistance, low probability of interception (LPI), fading mitigation and se-cure communications. Moreover, the non-periodic nature of chaotic codes adds further security and is a built-in feature of these codes Lynnyk & ˇCelikovsk`y (2010).

Furthermore, many studies that target the reduction of multi-user interference and PAPR show that chaotic sequences outperform sequences that have a periodic nature like Gold sequences Vitali et al. (2006).

To measure the performance of chaotic-based systems, a first study ever of the feasibility of using chaos shift keying (CSK) in a Multiple-Input Multiple-Output (MIMO) channels is cov-ered in Kaddoum et al. (2011), the integration of space-time block code (STBC) tehcniques into a CSK system is approached in Kaddoum & Gagnon (2013b) and a computation of the BER for asynchronous chaos-based DS-CDMA is provided in Kaddoum et al. (2009d). More-over, an investigation of the analysis of a cooperative decode-and-forward (DF) relay networks with chaos shift keying (CSK) modulation that constituted a first-ever application of CSK in the cooperative communications field is developed in Kaddoum & Gagnon (2013a).

An accurate approach to compute the bit error rate expression for the multiuser chaosbased DS-CDMA case is presented in Kaddoum et al. (2009b) and a comparison of different chaotic maps and their influence on the performance analysis of a direct-sequence code division multiple access (DS-CDMA) system when chaotic sequences are used instead of conventional pseudo-noise (PN) spreading codes is studied in Kaddoum et al. (2007).

Emphasizing that the application of chaos modulation in digital communications does not vio-late any basic principle, the potential use of chaotic signals in digital modulation is studied in Kaddoum et al. (2013c) and is found promising from an information theory point of view. Principally, two categories of chaos-based communication systems have been set forth for con-sideration:

- Coherently detected chaotic codes. In this layout, the receiver generates a synchronized copy of the chaotic signal and uses the generated replica in accordance with a detection technique to recover the transmitted data Kolumbán et al. (1997b).

The coherent reception is similar to replacing the conventional binary spreading sequences such as Gold, Walsh or pseudo-noise sequences by chaotic sequences, where the implementation of chaotic codes adds to security because of its non-periodic nature. This form of reception is used in chaos shift keying (CSK), chaos-based direct sequence code division multiple access (DS-CDMA), a configuration in which the chaotic signal is used to spread the data information signal while chaotic synchronization is required at the receiver side in order to regenerate an exact replica of the chaotic sequence to demodulate the transmitted bits Kaddoum et al. (2009c).

The chaotic symbolic dynamic (CSD) modulation has also been introduced as an important class of coherent chaotic modulation in Kurian et al. (2005) and a spread spectrum commu-nication system using chaotic symbolic dynamics modulation is studied in Kaddoum et al.

15

(2013b). In this latter work, the authors combine spread spectrum and chaotic modulation for the sake of increased security in a multiuser environment. The feasibility of having chaos-based communication in a 2 by 2 MIMO system using Alamouti space-time codes is presented in Kaddoum et al. (2012b), and an enhanced transceiver design has been proposed in Kaddoum

et al. (2012a) to overcome the performance degradation that arises because of synchronization

in noisy environments.

- Non-coherently detected chaotic codes. In this strategy, the receiver recovers the trans-mitted data by detecting features of the received signal with no knowledge of neither the chaotic codes nor the channel state information Kennedy et al. (2000).

The fact that non-coherent reception requires neither synchronization of chaotic codes nor the knowledge of CSI makes this reception approach a resilient and robust one. Examples of techniques that depend on non-coherent reception are differential chaos shift keying (DCSK) systems and chaos-based on off Keying (COOK) systems Kaddoum (2016b).

Additionally, an improved continuous-mobility differential chaos-shift-keying system (CM-DCSK) that provides improved performance in fast fading channels without accurate channel estimation is presented in Escribano et al. (2016) and a secure Multi-Carrier Differential Chaos Shift Keying (MC-DCSK) system in which a hybrid of MC modulation and DCSK is used is proposed in Kaddoum & Gagnon (2012). Besides, the application of chaos modulation has grown to include fields like power line applications Kaddoum & Tadayon (2017) and relay-based communication systems Kaddoum et al. (2014).

The concept has also been extended to energy harvesting, where a simultaneous wireless in-formation and power transfer scheme for short reference DCSK communication systems to overcome limited energy needs is provided in Kaddoum et al. (2017).

0.7 The Application of Index Modulation to Chaotic Modulation

Index modulation in chaotic systems is to use a certain property of chaotic sequences to ferry extra information per transmission, seeking further security, energy- and spectral- efficiency. Since the combination of IM and chaotic modulation techniques remains open, new forms and designs may be achieved. Here, we have a look at the studies carried out in this field.

0.7.1 Non-coherent Chaotic Index Modulation

Many works have considered IM for non-coherent chaotic modulation. The works called Car-rier Index Differential Chaos Shift Keying Modulation Cheng et al. (2017) and Permutation Index Differential Chaos Shift Keying (PI-DCSK) modulation that targets enhanced data se-curity and improved energy and spectral efficiencies Herceg et al. (2017) constitute prominent examples. In the PI-DCSK scheme, each data frame is divided into two time slots in which the reference chaotic signal is sent in the first time slot and a the product of the permuted replica of the reference signal into the modulating bit is sent in the second time slot. In particular, the bit stream is divided at the transmitter into blocks of n+ 1 bits, where n mapped bits are used to select one of the predefined reference sequence permutations, while a single modulated bit is spread by the permuted reference signal just mentioned. At the receiver side, the reference sig-nal is recovered first, then all permuted versions of it are correlated with the data bearing sigsig-nal. The index of the correlator output with the maximum magnitude will estimate the mapped bits, while the output of the corresponding correlator is compared to a zero threshold to recover the modulated bit. This technique may also be extended to the multiple access (MA) case.

With respect to hybrid modulation, a differentially spatial modulated chaos shift keying mod-ulation communication system where a part of outgoing symbols at the transmitter map an antenna index for transmission is proposed in Hu et al. (2017).

17

0.7.2 Coherent Chaotic Index Modulation

The application of index modulation to coherent chaotic schemes can enhance the data rate and enjoys the properties offered by these coherent schemes such as excellent performance, and high security. In fact, the coherent chaotic index modulation has followed the application of various index modulation techniques like SM, CIM, FIM and PI-DCSK. In particular, we have applied for the first time the index modulation to a coherent secure chaos-based scheme named chaos shift keying (CSK) in Soujeri et al. (2018). This unique scheme termed initial condition-index CSK (ICI-CSK) aspires the enhancement of spectral and energy efficiencies. In this vein, the proposed ICI-CSK scheme exploits the chaotic maps sensitivity on initial conditions to generate a large number of uncorrelated chaotic signals from the same chaotic map. In particular, at the transmitter, the data stream is formed in blocks of ptot = n + 1 bits

where the first n bits select an initial condition index from a set of N available initial conditions used to generate a chaotic sequence of a predetermined length, while the remaining single bit is spread by the selected chaotic sequence.

In this Thesis, we consider index modulation for both coherent and non-coherent chaotic re-ception schemes.

0.8 Author Contributions

Besides the papers that constitute the core of this Thesis, the author of this Thesis has been involved in and contributed to many other scientific papers not included in this Thesis. The contribution varied from a paper to another and took many forms, from partially performing simulation to verifying the integrity of the article, checking math, editing content, linguistic verification, cross-checking references and auditing survey.

The articles to which the Author has contributed so far, before the publication of this Thesis, are as listed here:

A. Conference Articles:

Georges Kaddoum, Navid Tadayon and Ebrahim Soujeri, 2016. « Performance of DCSK sys-tem with blanking circuit for power-line communications ». Proceedings of IEEE International Symposium on Circuits and Systems (ISCAS), Montreal, Canada, May 22-25, 2016.

Georges Kaddoum and Ebrahim Soujeri, "On the Comparison Between Code-Index Modula-tion and Spatial ModulaModula-tion Techniques", ICTRC 2015, UAE, 17-19 May 2015, pages 1-4.

B. Journal Articles:

Minh Au, Georges Kaddoum, François Gagnon and Ebrahim Soujeri, "A Joint Code-Frequency Index Modulation for Low-complexity, High Spectral and Energy Efficiency Communica-tions", IEEE Transactions on Communications, submitted: Dec 2017.

Marijan Herceg, Denis Vranješ, Georges Kaddoum and Ebrahim Soujeri, "Commutation Code Index DCSK Modulation Technique for High-Data-Rate Communication Systems", IEEE Trans-actions on Circuits and Systems II: Express Briefs, 2018. DOI: 10.1109/TCSII.2018.2817930

Marijan Herceg, Georges Kaddoum, Denis Vranješ and Ebrahim Soujeri,"Permutation Index DCSK Modulation Technique for Secure Multi-User High-Data-Rate Communication

Sys-19

tems", IEEE Transaction on Vehicular Technology, November 2017.

Georges Kaddoum and Ebrahim Soujeri, "NR-DCSK: A Noise Reduction Differential Chaos Shift Keying System", IEEE Transactions on Circuits and Systems II: Express Briefs, Year: 2016, Volume: PP, Issue: 99 Pages: 1 - 1, DOI: 10.1109/TCSII.2016.2532041.

Georges Kaddoum, Ebrahim Soujeri and Yogesh Nijsure, "Design of a Short Reference Nonco-herent Chaos-Based Communication Systems", IEEE Transactions on Communications, Year: 2016, Volume: 64, Issue: 2 Pages: 680 - 689, DOI: 10.1109/TCOMM.2015.2514089.

Georges Kaddoum, Ebrahim Soujeri, Carlos Arcila and Khaled Eshteiwi, "I-DCSK: An Im-proved Non-Coherent Communication System Architecture", IEEE Trans. on CAS II, 2015.

0.9 Thesis Outline

This Thesis is organized as follows:

Chapter 1 discusses the impact of antenna switching time on the performance of SM tech-niques. This is to show the cost associated with the implementation of SM techniques and the unsuitability of this technique to IoT and WSN applications. In Chapter 2, we study the frequency index modulation technique as a soft indexing substitute for the SM technique. In Chapter 3, we investigate initial condition index chaos shift keying modulation for high data rate, secure and high energy efficiency communications. This represents an example of the application of coherent CSK technique to index modulation. We also consider permutation in-dex DCSK modulation as an example of noncoherent DCSK application to inin-dex modulation,

that is placed in Appendix II. Finally, we have concluded this Thesis, included discussion and future work proposals in Conclusion and Recommendations.

CHAPTER 1

THE IMPACT OF ANTENNA SWITCHING TIME ON SPATIAL MODULATION Ebrahim Soujeri1, Georges Kaddoum1

1_{Department of Electrical Engineering, École de Technologie Supérieure,}

1100 Notre-Dame West, Montreal, Quebec, Canada H3C 1K3 Paper published in IEEE Wireless Communications Letters, June 2016.

Abstract

Spatial Modulation (SM) is an emerging technology that reduces hardware complexity, power consumption, inter-channel interference and antenna synchronization problems of multiple-input multiple-output (MIMO) communications. However, SM depends on continuous antenna transitions that rely on RF antenna switches which consume considerable time. Because of this, the data rates of SM schemes face a cap and are bound to certain limitations and the effective SM transmission is much less than the nominal value. In this letter, we study the impact of switching time on SM and we develop expressions for the effective transmission rate, effective capacity and spectral efficiency. An upper bound on the switching time is derived such that SM sustains capacity superiority in comparison with SIMO systems.

1.1 Introduction

Spatial modulation (SM) is an antenna-transition-based scheme that has been developed in the last decade Mesleh et al. (2008); Jeganathan et al. (2008b) with unique features. Data rate increment achieved via the utilization of the index of actively transmitting antenna is the core of this modulation scheme. Other benefits of using such modulation schemes comprise improved capacity, spectral and energy efficiency, the reduction to a single RF chain and the removal of inter-channel interference and inter-antenna synchronization requirements. Despite the existence of some drawbacks in this system like the absolute reliance of its performance on channel state information (CSI), i.e. being sensitive to channel correlation and erroneous

CSI Soujeri & Kaddoum (2015), it has been the focus of many research studies in the last decade. While bit error rate (BER) performance evaluation has received most attention, very little has been discussed about antenna transitions that constitute a critical property of SM systems. In fact, a study of MIMO antennas for mobile handsets has been carried out in Shoaib

et al. (2015) where the isolation properties of decoupling mechanism of certain antennas are

discussed. In this regard, parasitic antennas which rely on Micro Electro Mechanical Systems (MEMS) technology for RF applications are already being used in handheld mobile devices. Further, the switching time in MEMS technology is known to be in the range of 2− 50μs which renders it inefficient for today’s high-speed applications. Indeed, since SM may require a transition (switching) to happen for the transmission of each individual symbol to materialize, it is clear that switching times in antenna controllers must be significantly smaller than the symbol period. This requirement puts the option of MEMS-based switching technology off the table. According to Kalis et al. (2014), parasitic antenna arrays for MIMO applications using semiconductor diodes faster than 0.1μs (100 ns) are available. While in Ishibashi & Sugiura (2014), the effects of antenna switching on band-limited spatial modulation is investigated, where the employment of an SM-specific practical time-limited shaping filter is taken into account and the use of multiple RF chains is considered to transmit the side-lobes of band-limited pulses, in many recent works, i.e. Serafimovski et al. (2013) and Di Renzo et al. (2014), this issue has never been tackled or debated. This work is the first in this regard to shed the light on the feasibility of implementation of SM technology under the speed constraints of currently existing antenna switching technologies.

Contributions

Encouraged by the fact that RF antenna switches constitute an important part of the RF front end Bowick (2011) utilized in SM systems and we admit that these RF switches are neither cost-free nor steeply climbing (in zero-time) and require certain advanced technologies to per-form, i.e. acknowledging that switching time intervals introduce systematic transmission gaps in SM systems which overshadow its overall communication performance. In this letter, we

23

calculate the effective data rate, the effective capacity and the spectral efficiency of SM sys-tems for the first time under this practical constraint. In fact, we explore the speed limitations of industrial RF switches to analyse the SM system and to develop expressions for the effective data rate, effective capacity and spectral efficiency. We also identify the upper bound on the switching time interval such that the capacity superiority of SM with respect to single antenna transmission systems is sustained.

1.2 System Model

In SM, bits to be transmitted are grouped into m+ nt blocks, where the information is trans-mitted via Nt = 2nt number of antennas, where each antenna is loaded with a symbol from the constellation pool that has a size of 2m Mesleh et al. (2008); Jeganathan et al. (2008b). We add that the SM scheme would be equipped with an RF switch at the transmitter in the fashion shown in Fig. 1.1. Further details on RF switching can be found in CEL (2015) and in

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Figure 1.1 Block diagram of the SM transmitter

nxp (2014), and are omitted from this letter for lack of space. Literally, the fastest RF switch fabricated today has a switching time of 20 ns.

1.3 Analytical View

In an RF front end, we view the switching time as the time needed for the RF switch to forward an incoming signal to an antenna on one of its branches. In an SM system with Nt antennas at the transmitter, the process of choosing an antenna at every transmission period is a mutually exclusive event that follows a discrete uniform distribution. Since the antenna index is chosen from a constellation, a given antenna, i.e. the kth antenna is chosen with a probability of

Ps= Pr(a = ak) = 1/Nt, (1.1)

where Ps denotes the probability that the transmission stays on the kth antenna to transmit the next symbol, i.e. no switching happens. Likewise, the probability of switching to another antenna Pswto transmit the next symbol would become

Psw= 1 − Ps= 1 − 1/Nt. (1.2)

In fact, (1.2) shows the probability of hopping or jumping to another antenna in a set of Nt antennas. Considering these two probabilities and the fact that if a switching occurs then the symbol duration will be the switching time plus the SM symbol time, i.e. Tsw+ Ts, we may now discuss the effective SM symbol duration Tavwhich we define as

Tav≡ Ps· _Ts

(duration if not switching)

+Psw· (T_{  }s+ Tsw)

(duration if switching)

(1.3)

which, after substituting (1.1) and (1.2) into (1.3), may expand as

Tav= (Ts+ Tsw)Nt− Tsw

Nt .

(1.4)

As observed in (1.4), the effective SM symbol duration depends on the number of antennas involved in transmission and on the switching time in relationship with the RF switch. On the one hand, it is clearly noticed that Tav reduces to Tav= Ts in the hypothetical case of Tsw= 0.

25

This hypothesis is, however, unachievable in practical systems. On the other hand, a practical implementation of some SM receivers may require the insertion of a vacant pause of duration

Tsw whether or not switching takes place, to maintain synchronization and to avoid receiver oversampling of the received signals which may complicate the reception process. Hence, this hardware configuration can by analysed with the given analytical models by letting Ps= 0 and

Psw= 1 in (1.3), or equivalently, by having Nt very large in (1.4). Moreover, the performance of this SM system configuration is discussed in the discussion and simulation results section (section IV). Considering (1.4), the effective data rate Ref of SM will be expressed in symbols

per second (sps) as Ref= 1/Tav= Nt (Ts+ Tsw)Nt− Tsw sps. (1.5) 1.3.1 Effective SM Capacity

We use the conventional information theory approach Prisecaru (2010) to calculate the capacity of SM systems as C_SM =m+ nt  1+ pelog₂(pe) + pclog₂(pc) bpcu (1.6)

where perepresents the probability of error of SM detection in fading channels, pc= 1 − peis the probability of correct detection and m+ nt represents the total number of bits conveyed by the SM system, where m bits choose a constellation symbol and nt bits choose an antenna for transmission. Furthermore, the capacity of SM is not calculated the way it is done for MIMO communications, this is because the calculation of MIMO capacity CMIMO does not apply

Prisecaru (2010). In fact, the antenna number in SM represents added information and the antenna pattern is considered as spatial constellation, not as an information source as in MIMO. Moreover, other forms of determining the SM capacity based on mutual information may also be found in An et al. (2015). Note that pe is calculated in a fading channel environment since SM is not defined for AWGN channels in which it is impossible to detect the antenna indices

which require the uniqueness of channel coefficients. Ideally, the achievable SM data rate Rs would be

Rs≤ CSM, (1.7)

where Rs= 1/Tsand in practical situations where Tsw= 0, the effective SM data rate would be bounded as

R_ef≤ C_ef, (1.8)

where C_ef is the effective capacity. Dividing (1.8) by (1.7) and considering the equality to compute an upper bound, we may now without loss of generality express Cef in terms of CSM

in combination with (1.5) and (1.6) as

Cef= Ref/Rs·CSM = NtTs (Ts+ Tsw)Nt− Tsw·CSM = 1 1+ (1 − 1/Nt)β ·CSM (1.9)

whereβ = Tsw/Tsin (1.9) plays a fundamental role in determining the effective capacity for a given SM configuration with Nt transmitting antennas. It is also crucial to note that

lim

β→0Cef= CSM. (1.10)

1.3.2 Restrictions onβ

Using (1.9) along with Soujeri & Kaddoum (2015); Tse & Viswanath (2005) we may state the following order: C_SIMO≤ C_ef≤ C_SM≤ C_MIMO, where C_SIMOis the capacity of SIMO sys-tems. Note that ifβ grows then Cef will drop even below CSIMOand as a result, the capacity

gain achieved by SM will be lost which renders this modulation scheme useless and obsolete. Therefore, it is crucial to find a threshold value βth that will keep Cef above CSIMO such that

investing in SM systems would be feasible from the capacity point of view. In order to find the threshold valueβth that achieves this, we proceed following the requirement that CSIMO≤ Cef

27

where for Ntdegrees of freedom, CSIMOis calculated as described by (8.33) in Tse & Viswanath

(2005) and Cef is calculated according to (1.6) and (1.9). Noting the above, we pursue as

1

1+ (1 − 1/Nt)β ·CSM≥ CSIMO (1.11)

which results in the followingβ values

β ≤ βth= Nt Nt− 1 _C SM−CSIMO CSIMO (1.12)

and this forces Tswto remain capped in the range

Tsw≤ TsNt Nt− 1 _C SM−CSIMO CSIMO . (1.13)

Note that (1.13) above is extremely important and shows a critical relationship between the switching time Tsw and the symbol period Ts if SM capacity achievement is to be retained. As a matter of fact, (1.13) introduces an upper bound on the switching time Tsw in terms of the SM symbol duration Ts such that the capacity achievement of SM, as a system that uses multiple antennas to enhance capacity, in comparison to single-antenna systems is to preserve its superiority. Moreover, the upper bound on the switching time for a given scenario involves the calculation of CSMand CSIMOas described earlier under similar channel conditions.

1.3.3 Spectral Efficiency

For an SM symbol with duration Ts, the raised cosine filter occupies a bandwidth BSMfor each

pulse Ishibashi & Sugiura (2014) that is given by

BSM= (1 + α)/Ts, (1.14)

where 0 ≤ α ≤ 1. Keeping this in mind, we observe that switching introduces continuous vacant (empty) pauses in the time domain that interrupt and slow down the effective data rate. Note that while the SM system occupies a bandwidth BSM as indicated in (1.14) its effective

data rate reduces as given in (1.5). Inspired by Chung et al. (2007), we calculate the spectral efficiencyη of our system as the effective data rate divided by the bandwidth as

η (β) ≡ Ref B_SM = Nt (Ts+ Tsw)Nt− Tsw  _T s 1+ α = Nt Nt+ β(Nt− 1)  ₁ 1+ α . (1.15)

The spectral efficiency described in (1.15) is expected to degrade and vanish for large values

ofβ since

lim

β→∞η = 0, (1.16)

and to become inversely proportional toβ for large Nt as

ηmin= lim_N

t→∞η =

1

(1 + β)(1 + α). (1.17)

Furthermore, the maximum achievable spectral efficiency is independent of Ntand only occurs in the ideal case, i.e.

ηmax = η|β=0 = 1

(1 + α), (1.18)

however, the spectral efficiency can never reach unity in practical systems because neither the switching time Tsw nor the roll-off factorα are zero.

1.4 Discussions and Numerical Results

Switching time has an undeniable direct influence on the achievable data rate, spectral effi-ciency and capacity. The results obtained in this work confirm that industrial RF switches which are known to have a quantified and limited transition speed, impose an upper bound on the achievable data rate. In other words, moving to higher data rates will only be possible with advancements in RF switching technology, specifically from the switching speed point of view. Our results concerning the effects of switching time on these parameters will be presented in

29

the remaining part of this letter. Fig. 1.2 shows the effective SM transmission rate in mega symbols per second (Msps) in realistic scenarios at various RF switching speeds for Nt = 4 and 16 antennas. Judged by the wide gap in the effective SM data rates for Tsw = 0 and

0 10 20 30 40 50 60 70 80 90 100 0 10 20 30 40 50 60 SM symbol rate (Msps) Effective SM tr ansmission r a te ( M sps) T sw= 0, any Nt T sw= 10 ns, Nt=4 T sw= 20 ns, Nt=4 T sw= 50 ns, Nt=4 T sw= 10 ns, Nt=16 T sw= 20 ns, Nt=16 T sw= 50 ns, Nt=16

Figure 1.2 The effective SM data rate versus SM symbol rate

Tsw= 20 ns (the fastest RF switch available today), the important message that is conveyed by Fig. 1.2 is that ignoring Tsw leads to unrealistic transmission rate expectations. It is also observed that as Nt increases the effective data rate decreases, since the probability of hopping to a different transmitting antenna at every transmission instant rises. In Fig. 1.3, the capacities of MIMO, SIMO and SM are shown where the capacities of MIMO and SIMO are reproduced using the formulations given in Tse & Viswanath (2005) at SNR= 0 dB in a fading channel. The capacity of SM is calculated according to (1.6) where pe is based on the optimum maxi-mum likelihood (ML) detection outcome at the same SNR with a modulation order of M= 8, i.e. m= 3. Note that since Nt has to be a power of 2 in SM systems, we have compared the capacity of SM with the rival systems at these values of Nt only. Moreover, the relationship

Nt= Nris preserved in order to have a fair comparison between SM and MIMO systems given in Tse & Viswanath (2005). Table 1.1 shows capacity and switching parameters versus antenna configurations. As seen in Fig. 1.3, longer SM switching times cause Cef to reduce to the